WiscPlan_v2/WiscPlanPhotonkV125/matlab_frontend/NLP_optimizer_v3.m

% paths.patient_dir
% paths.Goal_dir (previously called DP_dir)
% paths.patient
% paths.goalsName

% colorwash(Geometry.data, D_full, [500, 1500], [0,70])
% orthoslice(D_full, [0,70])

function [D_full, w_fin, Geometry, optGoal] = NLP_optimizer_v3(varargin)
% This function performs the beamlet optimization
% [D_full, w_fin, Geometry, optGoal] = NLP_beamlet_optimizer;
% 
% Inputs:
%       () OR
%       (Pat_path, path2goal) OR
%       (Pat_path, path2goal, beamlet_weights)
%   Pat_path, path2goal = strings to patient folder and optimal goals
%   beamlet_weights = initial beamlet weights
%   
% Outputs:
%       full dose image dose: [D_full, w_fin, Geometry, optGoal]
% 
% Made by Peter Ferjancic 1. May 2018
% Last updated: 1. April 2019

if nargin<2
    load('WiscPlan_preferences.mat')
    [Pat_path] = uigetdir([WiscPlan_preferences.patientDataPath ], 'Select Patient folder');
    [Goal_file,Goal_path,indx] = uigetfile([Pat_path '\matlab_files\*.mat'], 'Select OptGoal file');
    
    path2geometry = [Pat_path, '\matlab_files\Geometry.mat'];
    path2goal = [Goal_path, Goal_file];
else
    Pat_path = varargin{1};
    path2geometry = [Pat_path, '\matlab_files\Geometry.mat'];
    path2goal = varargin{2};
    [Goal_path,Goal_file,ext] = fileparts(path2goal);
end

dialogue_box = 'no'
switch dialogue_box
    case 'yes'
        str = inputdlg({'N of iterations for initial calc', 'N of iterations for full calc', ...
            'Use pre-existing NLP_result to initiate? (y/n)'}, 'input', [1,35], {'100000', '500000', 'n'});
        N_fcallback1 = str2double(str{1}); % 100000  is a good guesstimate
        N_fcallback2 = str2double(str{2}); % 500000 is a good guesstimate
        pre_beamWeights = str{3};
    case 'no'
        disp('dialogue box skipped')
        N_fcallback1 = 100000;
        N_fcallback2 = 500000;
        pre_beamWeights = 'n';
end


switch pre_beamWeights
    case 'y'
        [NLP_file,NLP_path,indx] = uigetfile([Pat_path '\matlab_files\*.mat'], 'Select NLP_result file');
        load([NLP_path, NLP_file])
        w_beamlets = NLP_result.weights;
        
        load([Pat_path, '\all_beams.mat'])
        if numel(all_beams) ~= numel(w_beamlets)
            error('Provided weight number does not match beamlet number!')
        end
    case 'n'
        disp('Initial beam weights will be calculated.')
end

%% PROGRAM STARTS HERE
% - no tocar lo que hay debajo -
fprintf('starting NLP optimization process... \n')

% % -- LOAD GEOMETRY, GOALS, BEAMLETS --
load(path2geometry)
load(path2goal)
[beamlets, numBeamlet] = get_beamlets(Geometry, Pat_path, OptGoals);
% [beamlets, beamlets_joined, numBeamlet, numBeam, beam_i_list] = get_beam_lets(Geometry, Pat_path);


%% -- OPTIMIZATION TARGETS --
% -- make the optimization optGoal structure --
for i_goal = 1:size(OptGoals.goals,1)
        
    if isfield(OptGoals.data{i_goal}, 'SupVox_num')
        SupVox_num = OptGoals.data{i_goal}.SupVox_num;
    else
        answer = inputdlg(['# of supervoxels for "' OptGoals.data{i_goal}.name '" with ' num2str(numel(OptGoals.data{i_goal}.ROI_idx)) ' vox: ("0" to skip)'])
        SupVox_num = str2double(answer{1})
    end
    optGoal{i_goal} = OptGoals.data{i_goal};
    optGoal{i_goal}.sss_scene_list = OptGoals.sss_scene_list;
    optGoal{i_goal}.maxModulation = OptGoals.maxModulation;
    optGoal{i_goal}.BeamSmoothMax = OptGoals.BeamSmoothMax;
    
    % modulation
    switch SupVox_num
        case 0
        % if not supervoxel, just select provided ROI_idx
        
        optGoal{i_goal}.beamlets_pruned = sparse(beamlets(optGoal{i_goal}.ROI_idx, :));
    
        otherwise
        % -- if supervoxel, merge given columns
        % - make supervoxel map
        mask = zeros(OptGoals.data{i_goal}.imgDim);
        mask(OptGoals.data{i_goal}.ROI_idx) = 1;
        % group superpixels
        superMask = superpix_group(mask, SupVox_num, 'no'); 
        
        superVoxList = unique(superMask);
        superVoxList = superVoxList(superVoxList>0);
        
        optGoal{i_goal}.ROI_idx_old = optGoal{i_goal}.ROI_idx; % copy old index data
        optGoal{i_goal}.ROI_idx = zeros(numel(superVoxList), 1);
        optGoal{i_goal}.opt_weight = optGoal{i_goal}.opt_weight * numel(optGoal{i_goal}.ROI_idx_old)/numel(optGoal{i_goal}.ROI_idx);
        
        if isfield(OptGoals.data{i_goal}, 'wgt_map')
            tabula_wgtmap = zeros(size(superMask));
            tabula_wgtmap(OptGoals.data{i_goal}.ROI_idx) = OptGoals.data{i_goal}.wgt_map;
        end
        
        
        
        h_w1 = waitbar(0, 'merging superboxels');
        for i_supVox = 1:numel(superVoxList)
            waitbar(i_supVox/numel(superVoxList), h_w1)
            supVox_idx = superVoxList(i_supVox);
            idxList = find(superMask == supVox_idx);
            optGoal{i_goal}.beamlets_pruned(i_supVox,:) = sparse(mean(beamlets(idxList, :),1));
            
            if isfield(OptGoals.data{i_goal}, 'wgt_map')
                optGoal{i_goal}.vox_wgt(i_supVox) = sum(tabula_wgtmap(idxList));
            end
            
            % -- make new indeces
            optGoal{i_goal}.ROI_idx(i_supVox) = idxList(1);
        end
        close(h_w1)
    end
end

% -- make them robust --
RO_params=0;
optGoal = make_robust_optGoal(optGoal, RO_params, beamlets);
% save([Goal_path, Goal_file '_robust.mat'], 'optGoal')

% -- get beamlet indeces --
load([Pat_path, '\all_beams.mat'])
Nbeamlets = all_beams{1}.Mxp;   % number of beamlets in a beam - usually 64 or 32
weightTable = zeros(100,Nbeamlets);
for ind_bmlt = 1:numel(all_beams)
    bLet_idx.y(ind_bmlt) = floor(all_beams{1, ind_bmlt}.num/Nbeamlets)+1;
    bLet_idx.x(ind_bmlt) = rem(all_beams{1, ind_bmlt}.num, Nbeamlets)+1;
    weightTable(bLet_idx.y(ind_bmlt),bLet_idx.x(ind_bmlt)) = 1;
end
bLet_idx.idx = find(weightTable>0);
bLet_idx.Nbeamlets = Nbeamlets;
disp('.')

% -- CALLBACK OPTIMIZATION FUNCTION --
fun1 = @(x) get_penalty(x, optGoal_beam, bLet_idx);
fun2 = @(x) get_penalty(x, optGoal,     bLet_idx);

% -- OPTIMIZATION PARAMETERS --
% define optimization parameters
A = [];
b = [];
Aeq = [];
beq = [];
lb = zeros(1, numBeamlet);
% lb_beam = zeros(1, numBeam);
ub = [];
nonlcon = [];

% define opt limits, and make it fmincon progress
options = optimoptions('fmincon');
options.MaxFunctionEvaluations = N_fcallback1;
options.Display = 'iter';
options.PlotFcn = 'optimplotfval';
% options.UseParallel = true;
options.UseParallel = false;
% options.OptimalityTolerance = 1e-9;

%% -- INITIALIZE BEAMLET WEIGHTS --
switch pre_beamWeights
    case 'y'
        % should have been assigned previously.
        disp('Provided beamlet weights used for initial comparison')
    case 'n'
        % if initial beamlet weights are not provided, get quick estimate
%         fprintf('\n running initial optimizer:')
        % initialize beamlet weights, OR
        w0 = ones(numBeamlet,1);
%         w0 = mean(optGoal{1}.D_final(optGoal{1}.ROI_idx) ./ (optGoal{1}.beamlets_pruned*w0+0.1)) * w0; % old
        w0 = mean(optGoal{1}.D_final(:)) ./ mean(optGoal{1}.beamlets_pruned*w0+0.05) * w0;
        w_beamlets = double(w0);

        % -- GET BEAM WEIGHTS --
%         tic
%         w_beam = fmincon(fun1,w0_beams,A,b,Aeq,beq,lb,ub,nonlcon,options);
%         fprintf('  done!:')
%         t=toc;
%         disp(['Optimization time for beams = ',num2str(t)]);
% 
%         w_beamlets = ones(numBeamlet,1);
%         numBeam=numel(unique(beam_i_list));
%         for beam_i = 1:numBeam % assign weights to beamlets
%             % beamlets from same beam get same initial weights
%             w_beamlets(beam_i_list == beam_i) = w_beam(beam_i);
%         end
end

%% FULL OPTIMIZATION

% -- GET FULL BEAMLET WEIGHTS --
options.MaxFunctionEvaluations = N_fcallback2;
tic
fprintf('\n running full optimizer:')
w_fin = fmincon(fun2,w_beamlets,A,b,Aeq,beq,lb,ub,nonlcon,options);
fprintf('  done!:')
t=toc;
disp(['Optimization time for beamlets = ',num2str(t)]);


%% evaluate the results
D_full = reshape(beamlets * w_fin, size(Geometry.data));

%% save outputs
NLP_result.dose = D_full;
NLP_result.weights = w_fin;
NLP_result.sss_scene_list = optGoal{1}.sss_scene_list;
NLP_result.maxModulation = OptGoals.maxModulation;
NLP_result.BeamSmoothMax = OptGoals.BeamSmoothMax;
save([Pat_path, '\matlab_files\NLP_result_' Goal_file '.mat'], 'NLP_result');


plot_DVH(Geometry, D_full)
colorwash(Geometry.data, D_full, [500, 1500], [0, 90]);


end

%% support functions
% ---- PENALTY FUNCTION ----
function penalty = get_penalty(x, optGoal, bLet_idx)
    % this function gets called by the optimizer. It checks the penalty for
    % all the robust implementation and returns the worst result.
    
    NumScenarios = optGoal{1}.NbrRandScenarios * optGoal{1}.NbrSystSetUpScenarios * optGoal{1}.NbrRangeScenarios;
    fobj = zeros(NumScenarios,1);  
    sc_i = 1;
    

    
    for nrs_i = 1:optGoal{1}.NbrRandScenarios 
        for sss_i = 1 :optGoal{1}.NbrSystSetUpScenarios % syst. setup scenarios = sss
            for rgs_i = 1:optGoal{1}.NbrRangeScenarios % range scenario = rs
                fobj(sc_i)=eval_f(x, optGoal, nrs_i, sss_i, rgs_i, bLet_idx);
                sc_i = sc_i + 1;
            end
        end
    end
    % take the worst case penalty of evaluated scenarios
    penalty=max(fobj);
    
    % take the median worst case (stochastic robust)
%     penalty=median(fobj);


    
end
% ------ supp: penalty for single scenario ------
function penalty = eval_f(x, optGoal, nrs_i, sss_i, rgs_i, bLet_idx)
    penalty = 0;
    % for each condition
    for goal_i = 1:numel(optGoal)
        switch optGoal{goal_i}.function
            % min, max, min_sq, max_sq, LeastSquare, min_perc_Volume, max_perc_Volume
            case 'min'
                % penalize if achieved dose is lower than target dose
                d_penalty = 1.0e0 * sum(max(0, ...
                    (optGoal{goal_i}.nrs{nrs_i}.sss{sss_i}.rgs{rgs_i}.target) -...
                    (optGoal{goal_i}.nrs{nrs_i}.sss{sss_i}.rgs{rgs_i}.beamlets_pruned * x)));
            case 'max'
                % penalize if achieved dose is higher than target dose
                d_penalty = 1.0e0 * sum(max(0, ...
                    (optGoal{goal_i}.nrs{nrs_i}.sss{sss_i}.rgs{rgs_i}.beamlets_pruned * x)-...
                    (optGoal{goal_i}.nrs{nrs_i}.sss{sss_i}.rgs{rgs_i}.target)));
            case 'min_sq'
                % penalize if achieved dose is lower than target dose
                temp1=min(0, (optGoal{goal_i}.nrs{nrs_i}.sss{sss_i}.rgs{rgs_i}.beamlets_pruned * x)-...
                    (optGoal{goal_i}.nrs{nrs_i}.sss{sss_i}.rgs{rgs_i}.target));
                d_penalty = 1.0e0 * sum(temp1.*temp1);
            case 'max_sq'
                % penalize if achieved dose is higher than target dose
                temp1=max(0, (optGoal{goal_i}.nrs{nrs_i}.sss{sss_i}.rgs{rgs_i}.beamlets_pruned * x)-...
                    (optGoal{goal_i}.nrs{nrs_i}.sss{sss_i}.rgs{rgs_i}.target));
                d_penalty = 1.0e0 * sum(temp1.*temp1);
            case 'min_step'
                % penalize if achieved dose is lower than target dose
                temp1=-min(0, (optGoal{goal_i}.nrs{nrs_i}.sss{sss_i}.rgs{rgs_i}.beamlets_pruned * x)-...
                    (optGoal{goal_i}.nrs{nrs_i}.sss{sss_i}.rgs{rgs_i}.target));
                d_penalty = 1.0e0 * (sum(temp1) + numel(temp1)* any(temp1));
            case 'max_step'
                % penalize if achieved dose is higher than target dose
                temp1=max(0, (optGoal{goal_i}.nrs{nrs_i}.sss{sss_i}.rgs{rgs_i}.beamlets_pruned * x)-...
                    (optGoal{goal_i}.nrs{nrs_i}.sss{sss_i}.rgs{rgs_i}.target));
                d_penalty = 1.0e0 * (sum(temp1) + numel(temp1)* any(temp1));
            case 'LeastSquare'
                % penalize with sum of squares any deviation from target
                % dose
                temp1 = (optGoal{goal_i}.nrs{nrs_i}.sss{sss_i}.rgs{rgs_i}.beamlets_pruned * x) - ...
                    optGoal{goal_i}.nrs{nrs_i}.sss{sss_i}.rgs{rgs_i}.target;
                d_penalty = 1.0e0* sum(temp1.^2);
            case 'min_perc_Volume'
                % penalize by amount of volume under threshold
                perc_vox = numel(find((optGoal{goal_i}.nrs{nrs_i}.sss{sss_i}.rgs{rgs_i}.target) -...
                    (optGoal{goal_i}.nrs{nrs_i}.sss{sss_i}.rgs{rgs_i}.beamlets_pruned * x) > 0)) ...
                    / numel(optGoal{goal_i}.nrs{nrs_i}.sss{sss_i}.rgs{rgs_i}.target);
                d_penalty = 3.0e4 * min(perc_vox-0.05, 0)
                
            case 'max_perc_Volume'
                % penalize by amount of volume under threshold
                perc_vox = numel(find((optGoal{goal_i}.nrs{nrs_i}.sss{sss_i}.rgs{rgs_i}.target) -...
                    (optGoal{goal_i}.nrs{nrs_i}.sss{sss_i}.rgs{rgs_i}.beamlets_pruned * x) < 0)) ...
                    / numel(optGoal{goal_i}.nrs{nrs_i}.sss{sss_i}.rgs{rgs_i}.target);
                d_penalty = 3.0e4 * min(perc_vox-0.05, 0)
            case 'min_sq_voxwgt'
                % penalize if achieved dose is lower than target dose
                temp1=min(0, (optGoal{goal_i}.nrs{nrs_i}.sss{sss_i}.rgs{rgs_i}.beamlets_pruned * x)-...
                    (optGoal{goal_i}.nrs{nrs_i}.sss{sss_i}.rgs{rgs_i}.target));
                d_penalty = 1.0e0 * sum(temp1.*temp1.* optGoal{goal_i}.vox_wgt');
            case 'max_sq_voxwgt'
                % penalize if achieved dose is lower than target dose
                temp1=min(0, (optGoal{goal_i}.nrs{nrs_i}.sss{sss_i}.rgs{rgs_i}.beamlets_pruned * x)-...
                    (optGoal{goal_i}.nrs{nrs_i}.sss{sss_i}.rgs{rgs_i}.target));
                d_penalty = 1.0e0 * sum(temp1.*temp1.* optGoal{goal_i}.vox_wgt'); 
        end
        penalty = penalty + d_penalty * optGoal{goal_i}.opt_weight;
    end
    
    %% add modulation penalty
    if true
        if isfield(optGoal{goal_i}, 'maxModulation')
            max_modulation = optGoal{goal_i}.maxModulation;
        else
            error('no Max modulation parameter enterd!')
            max_modulation = 5;
        end
        
        mod_pen_weight = 1.0e10;
        % calc the penalty
        mod_excess = max(0, x-max_modulation*mean(x));
%         mod_excess = max(0, x-max_modulation*mean(x(x>1)));
        mod_pen1 = mod_pen_weight*(sum(mod_excess) + numel(mod_excess)* any(mod_excess));
        penalty = penalty + mod_pen1;
    end
    
    %% add penlty for single off beamlets - version 2
    if false
        if isfield(optGoal{goal_i}, 'BeamSmoothMax')
            BeamSmoothMax = optGoal{goal_i}.BeamSmoothMax;
        else
            error('no Max beam smooth parameter enterd!')
            BeamSmoothMax = 1e6;
        end
        mod_pen_weight = BeamSmoothMax; %1.0e6
        x_down = zeros(size(x));
        x_down(2:end) = x(1:end-1);
        x_down2 = zeros(size(x));
        x_down2(3:end) = x(1:end-2);
        x_up = zeros(size(x));
        x_up(1:end-1) = x(2:end);
        x_up2 = zeros(size(x));
        x_up2(1:end-2) = x(3:end);
        mod_pen2 = mod_pen_weight*sum((x_down+x_up-2*x).^2 + 0.5*(x_down2+x_up2-2*x).^2)/(mean(x)^(2)*numel(x));
        penalty = penalty + mod_pen2;
    end
    %% add penlty for single off beamlets - version 3
    if true
        if isfield(optGoal{goal_i}, 'BeamSmoothMax')
            BeamSmoothMax = optGoal{goal_i}.BeamSmoothMax;
        else
            error('no Max beam smooth parameter enterd!')
            BeamSmoothMax = 1e6;
        end
        mod_pen_weight = BeamSmoothMax; %1.0e6
        
        % make 2D beamletWeight map
        maxY = max(bLet_idx.y);
        tabula = zeros(maxY, bLet_idx.Nbeamlets);
        tabula(bLet_idx.idx) = x;
        % for each index calculate laplace
        myWeights = 1/12*[1,3,1; 1,-12,1; 1,3,1];
        i=2:maxY-1;
        j=2:bLet_idx.Nbeamlets-1;
        tabula2(i,j) = ...
             myWeights(1)*tabula(i-1,j-1) + myWeights(4)*tabula(i-1,j) + myWeights(7)*tabula(i-1,j+1)...
            +myWeights(2)*tabula(i,j-1)  + myWeights(8)*tabula(i,j+1) ...
            +myWeights(3)*tabula(i+1,j-1) + myWeights(6)*tabula(i+1,j) + myWeights(9)*tabula(i+1,j+1)...
            +myWeights(5)*tabula(i,j);
        tabula2(1,j) = ...
             myWeights(2)*tabula(1,j-1) + myWeights(8)*tabula(1,j+1)...
            +myWeights(3)*tabula(2,j-1) + myWeights(6)*tabula(2,j) + myWeights(9)*tabula(2,j+1)...
            +myWeights(5)*tabula(1,j);
        tabula2(maxY,j) =...
             myWeights(1)*tabula(maxY-1,j-1) + myWeights(4)*tabula(maxY-1,j) + myWeights(7)*tabula(maxY-1,j+1)...
            +myWeights(2)*tabula(maxY,j-1)  + myWeights(8)*tabula(maxY,j+1) ...
            +myWeights(5)*tabula(maxY,j);
        % make sum of squares
        mod_pen2 = mod_pen_weight*sum((tabula2(:)).^2)/(mean(x.^2)*numel(x));
        penalty = penalty + mod_pen2;
    end
end

% ---- MAKE ROI ROBUST ----
function optGoal = make_robust_optGoal(optGoal, RO_params, beamlets);
    % take regular optimal goal and translate it into several robust cases
    
    % RO_params - should have the information below
    % nrs - random scenarios
    % sss - system setup scenarios
    % rgs - random range scenarios
    
    % X - X>0 moves image right
    % Y - Y>0 moves image down
    % Z - in/out.
    
    shift_X = 2; % vox of shift
    shift_Y = 2; % vox of shift
    shift_Z = 1; % vox of shift
    nrs_scene_list={[0,0,0]};

    
    % ----====#### CHANGE ROBUSTNESS HERE ####====----
    if isfield(optGoal{1}, 'sss_scene_list')
        sss_scene_list = optGoal{1}.sss_scene_list;
    else
        sss_scene_list={[0,0,0], [-shift_Y,0,0], [shift_Y,0,0], [0,-shift_X,0], [0,shift_X,0], [0,0,-shift_Z], [0,0,shift_Z]};
        optGoal{1}.sss_scene_list = sss_scene_list;
    end
%     sss_scene_list={[0,0,0]};

    % ----====#### CHANGE ROBUSTNESS HERE ####====----
%     [targetIn, meta] = nrrdread('C:\010-work\003_localGit\WiscPlan_v2\data\archive\CDP_data\CDP5_DP_target.nrrd');
%     [targetIn, meta] = nrrdread('C:\010-work\003_localGit\WiscPlan_v2\data\PD_HD_dicomPhantom\Tomo_DP_target.nrrd');
%     [targetIn, meta] = nrrdread('C:\010-work\003_localGit\WiscPlan_v2\data\archive\CDP_data\CDP5_DP_target.nrrd');
    rgs_scene_list={[0,0,0]};
    for i = 1:numel(optGoal)
        optGoal{i}.NbrRandScenarios     =numel(nrs_scene_list);
        optGoal{i}.NbrSystSetUpScenarios=numel(sss_scene_list);
        optGoal{i}.NbrRangeScenarios    =numel(rgs_scene_list);
    end
    for goal_i = 1:numel(optGoal)
        % get target
        idx=optGoal{goal_i}.ROI_idx;
        targetImg1=zeros(optGoal{goal_i}.imgDim);
        targetImg1(idx)=1;
        % get beamlets
        for nrs_i = 1:optGoal{goal_i}.NbrRandScenarios          % num. of random scenarios
            % modify target and beamlets
            targetImg2=targetImg1;
            % beamlets stay the same
            for sss_i = 1 :optGoal{goal_i}.NbrSystSetUpScenarios   % syst. setup scenarios = sss
                % modify target and beamlets
                [targetImg3 idxValid]=get_RO_sss(targetImg2, sss_scene_list{sss_i});
                % beamlets stay the same
                for rgs_i = 1:optGoal{goal_i}.NbrRangeScenarios   % range scenario = rgs
                    % modify target and beamlets
                    targetImg4=targetImg3;
                    % beamlets stay the same
                    %% make new target and beamlets
                    ROI_idx=[];
                    ROI_idx=find(targetImg4>0);
                    target = optGoal{goal_i}.D_final(idxValid);
                    beamlets_pruned = beamlets(ROI_idx, :);
                    % save to optGoal output
                    optGoal{goal_i}.nrs{nrs_i}.sss{sss_i}.rgs{rgs_i}.ROI_idx            = ROI_idx;
                    optGoal{goal_i}.nrs{nrs_i}.sss{sss_i}.rgs{rgs_i}.beamlets_pruned    = beamlets_pruned;
                    optGoal{goal_i}.nrs{nrs_i}.sss{sss_i}.rgs{rgs_i}.target             = target;
                end
            end
        end
    end
end
%% ------ supp: RO case SSS ------
function [targetImg3 ia]=get_RO_sss(targetImg2, sss_scene_shift);
    % translate the target image 
    
    targetImg3 = imtranslate(targetImg2,sss_scene_shift);
    
    % now we need to figure out if any target voxels fell out during the
    % shift
    imgValid = imtranslate(targetImg3,-sss_scene_shift);
    imgInvalid = (targetImg2-imgValid);
    
    idx_1 = find(targetImg2);
    idx_2 = find(imgInvalid);
    
    [idxValid,ia] = setdiff(idx_1,idx_2);
    
    [C,ia, ib] = intersect(idx_1,idxValid);
    
end